關於 the changing world order ，我們在網路上蒐集到這些相關的討論、資訊與評價

Guard Your Heart with Psalm 91

“I will say of Yahweh, “He is my refuge and my fortress; my God, in whom I trust.” For he will deliver you from the snare of the fowler, and from the deadly pestilence. He will cover you with his feathers. Under his wings you will take refuge. His faithfulness is your shield and rampart. You shall not be afraid of the terror by night, nor of the arrow that flies by day; nor of the pestilence that walks in darkness, nor of the destruction that wastes at noonday. A thousand may fall at your side, and ten thousand at your right hand; but it will not come near you. You will only look with your eyes, and see the recompense of the wicked. Because you have made Yahweh your refuge, and the Most High your dwelling place, no evil shall happen to you, neither shall any plague come near your dwelling. For he will put his angels in charge of you, to guard you in all your ways. They will bear you up in their hands, so that you won’t dash your foot against a stone.” (Psalms‬ ‭91:2-12‬ ‭WEB‬‬)

Remember that true protection comes from the Lord. Meditate on the Scriptures and confess them over yourself and your loved ones. Guard your heart from the fear and worry that is being perpetuated by the media.

When you believe and speak God’s word, God’s power is released in that related area of your life. His words are spirit and life, not just inanimate ink on a page.

A refuge is a place that you flee to after being attacked, while a fortress is a place you can preemptively position yourself to be far from the enemy.

Whether you have been attacked or not, Jesus is your source of safety, protection, and healing.

Someone may say, “What about those Christians that got it? So many in that local church got sick. How can God’s promises be true?”

Well, one needs to believe in God’s promises before he will experience it. They do not manifest for a Christian who is unbelieving and stricken by fear.

We do not know their state of mind at the time when they fell sick, and what their local church teaches about God’s protection. Some do not believe in it.

I like that Psalm 91 specifically shows that we can believe God for protection from everything that the world is afraid of nowadays. We do not have to guess God’s will in this case—it is plainly written.

Even if you hear of news about people getting sick in your neighborhood, God’s word remains true: a thousand may fall at your side, and ten thousand at your right hand, but it shall not come near you.

The enemy probably hates it when you believe this. “What makes you think you are so special? Others are dying and in critical condition, and you have the cheek to say that it cannot come near you?”

You are specially protected if you believe in God’s promises. You are a sanctified child of God who has access to His protection by faith. His angels will be mobilized to guard you in all your ways, to destroy every weapon of the enemy near you.

Sometimes, believers who just stumbled and sinned feel unworthy of experiencing God’s protection. They feel like the hedge of protection has been lifted because they sinned and that God does this to teach them a lesson.

That is a false assumption that is not true under the New Covenant of Grace. Committing sin can cause your conscience to accuse you, but we must know that Grace is all about believing in what Jesus has done at the cross.

You can enjoy God’s protection from all manner of harm because Jesus shed His blood to make you forever righteous and favored in God’s sight. Protection is not a reward that you have to earn through good behavior. It is freely given as part of the salvation package—but you must believe in order to enjoy it!

Actionable Steps:

1. Meditate on Psalm 91 today and see which portion of it resonates deeply with you. Keep it in your heart and mutter it with your mouth throughout the week ahead.

2. Include words from Psalm 91 in your daily prayers for your family in the morning. Before everyone sets off for work or school, take time to tune everyone’s heart to be conscious of God’s lavish protection.

3. Look out for anyone you come across that feels unsafe or fearful because of the current situation. Encourage them with promises from Psalm 91 and tell them that Jesus loves them. There is always a good time to plant seeds of the Gospel in people’s hearts.

Our Patreon community is currently on a Bible Study series called “The Way Forward: How to Thrive Amidst Change”.

In a time of great fear, how can we as Christians thrive when the world is changing the way they do things? Many in the world are depressed and terrified because of the things that are happening around the world; the change ambushed most people so suddenly. Yes there is deep darkness covering the earth, but there is always hope for God’s children.

The Holy Spirit is giving us a word in season, showing us how to tap on the grace that is available now, and how to reign in life, even from your living room. I’m excited to see what He will show us in the days ahead!

This Bible Study series will be compiled into an eBook once we complete it.

Join us as a “God Every Morning” tier or above patron on Patreon to receive this new Bible Study series in our patron WhatsApp group chat. You will also receive the other rewards like devotionals by email every weekday, and all my eBooks. Thank you for sowing into this ministry and being a valuable partner as we “Teach More, Reach More” every day in these end times: http://Patreon.com/miltongohblog

【後疫情時代中國面對的經濟環境】

本文嘗試用一個廣角、簡略但直入重點的方式分析中國在疫情之後所面對的全球經濟環境。

國家競爭力的經濟學概念與中國縣競爭制度

根據經濟學比較優勢定理，國家之間的競爭始終被比較成本所局限。而在分析國家競爭力上，我摒棄華而不實的哈佛商學院Michael Poter的鑽石競爭理論，回歸最基本但正確的經濟學成本概念，其中尤受諾貝爾經濟學獎得主R. Coase的「The Problem of Social Costs」鴻文啓發：

國家競爭成本 = 直接生產成本 + 間接生產成本 + 制度費用

特別說明我所謂的「間接生產成本」更接近上頭成本，本身除了牽涉到整體租值外也會涉及到產業乃至於社會國家的路徑依賴。

在相同供應層面，某國是否可以用更低成本下滿足同樣的需求，以及是否可以善用比較優勢定理。後者包含了前者的同時，也是國家與國家之間的角色不單純只是競爭關係，而是有更多供需關係。後者之所以尤為重要在於「買方與賣方永遠不存在競爭關係」。因此在供應鏈上彼此依賴的買賣雙方國家，依賴程度越深入越廣泛，則敵對的成本將等比級數增加。

換個角度來說，Covid-19疫情本身帶來上述三種成本的同步增加。這也意味著在疫苗逐漸普及的後疫情時代，能夠以更快速地降低上述三種成本的國家將在新一輪全球經濟重新平衡的過程中取得更佳的競爭優勢地位。

在張五常「The Economic Structure of China」一書闡述的中國曾有的1990年代末到2010年間之縣競爭制度下，中國借此享受人類近代少有的超低制度費用與間接生產成本，佐以原本享有的人口紅利帶來的在中低階工廠流水線上較低直接生產成本，中國製造橫掃全世界九成以上的中低階工業領域。

但隨著中國中央政府出台勞動法與加強反托拉斯管制與大大小小的管制措施，上述獨有的縣競爭制度似乎已不復存在。這也為疫情後面對全世界新的經濟環境中國是否還具有經濟學謂「低制度費用」的高彈性與快速適應力埋下變數。

瞭解這個重要局限條件改變後，我們來看看疫情後中國所面對的全球經濟挑戰有哪些。

1 全球通貨膨脹可能帶給中國輸入性通膨

美國建國以來90%以上的M0貨幣發行量是在最近15年內產生，尤其疫情後Fed諸多舉措都可說是「瘋狂印鈔」，在世界多數原物料與貿易均以美元定價與結算的前提下，世界性通貨膨脹必然來到。

站在2021年5月這個時間點看，美國股市、房市、債市與全世界的大宗期貨、能源價格都受到局部性通膨影響，尤其主要農產品、金屬期貨價格多在52周以來新高。（見圖）

（美國M0通貨）

（美國股市）

（美國房市）

（美國債市）

（石油價格）

中國改革開放以來相當長一段時間貨幣匯率政策緊盯美元。2010年代以後雖然改盯一籃子貨幣，但明眼人都看得出美元的比重。故，在美元瘋狂印鈔的環境下，人民幣相應的輸入性通膨也必然發生。

這一塊我們可以預測，在貨幣學 Impossible trinity law的局限，以及中國對人民幣國際化的追求下，中國人民銀行應將在近年內逐步脫鈎對美元匯率的政策，同時部分放寬外匯管制，以得到更多貨幣主權。

同時取消或降低部分關稅，以及放寬戶口管制，都可以是中國政府提高國家競爭力可能採取的措施。

二、 全球局部地區將因疫情影響出現糧食危機

很明顯Covid-19疫情影響了糧食生產與輸布，全球局部地區的糧食危機已經開始出現。根據聯合國2020年糧食安全報告估計到2020年底全球因疫情而陷入經濟衰退與飢餓的人口數達8300萬～1.32億人。其引發的糧食價格增長將加重中國輸入性通膨下，百姓生活的負擔

中國家戶支出30%花費在食物品項，又中國國內大豆需求90%依賴進口滿足，因此可預見中國的飼料與肉品市場價格恐將上揚且吃緊。

（中國主要糧食供需狀況）

全球能源市場也會因疫情與之前負油價事件影響一段時間內失去部分供給彈性，意味著能源市場價格伴隨通膨因素影響的上揚也是可以預期，這一塊同樣也會加重中國未來將面對的輸入性通膨壓力。

因此我們會看到中國在人民幣國際化推廣上會施以更大力道，例如與更多國家簽訂貨幣清算與貨幣交換協議，嘗試在糧食/能源品項上更多地採人民幣定價結算。如此方可在不過度犧牲中國世界供應煉地位的前提下，減少輸入性通膨對人民的衝擊，尤其是輸入性通膨下中國國內資本投資的資源錯置現象將可以得到一定程度約束。當然這部分中國政府應該還會採取價格管制或其他市場管制措施相佐之，但政府干預與介入本身又會帶來更多訊息費用、交易費用，甚至政府本身就成為資源錯置的問題根本，也是極為可能。這些都是身為投資人的我們值得持續觀察與因應。

三、 中美衝突與戰爭風險提高

如前述，國家邊際競爭成本，尤其邊際間接生產成本與邊際制度費用，增加速率大過他國之速率，則一國之國力衰退，或更精准地說，國家相對競爭優勢衰退。反之則可視為國家相對競爭優勢增加。

在人民幣國際化過程將直接與美元產生競爭關係且削弱美國對全球徵收「美元稅」的能力，經濟邏輯上的效果是：2008年金融危機後的QE之所以沒有在美國發生嚴重通膨，正是因為美元在國際貿易與國際金融的霸主地位可以對全球抽取美元稅，意味著美國可以將貨幣濫發帶來的經濟成本移轉給全世界承擔，其中以世界貿易額佔比越高者承擔越多，故身為世界第一大商品出口國的中國自然也承擔大部分苦果，這也是為何我長時間以來主張美元的地位相當程度是由中國支撐。

而在人民幣競爭之下（我們假設人民幣國際化真取得成效），美國不再能輕易移轉自身國家競爭成本給全世界時，通貨膨脹將回歸隨著貨幣發行量增長而提高，這對美國而言代表聯邦政府與州政府等一系列債券、連動債務的利息支出成本將提高，未來借貸成本也將提高。在一定程度上，美國政府或州政府可能因此停擺，甚或我們會看到州政府、市政府因此破產。

因此美國必然會嘗試在各方面阻止之。

提高上述中國的國家邊際競爭成本也無可避免會是美國未來數十年的整體戰略目標。

所以我們看到美國從President Trump任期開始，嘗試尋找各種可以提高中國國家邊際競爭成本的手段。

然而在當今真實世界供應煉、服務煉、金流、資訊流高度分工交雜的局限條件下，我推斷任何一任美國政府、智庫都難以清楚釐清自身採取的任何競爭戰略是否會帶來意料之外的後果（unintentional consequences）。

a 舉例來說，比如美國政客錯誤判斷關稅手段制裁中國會有效，於是我們看到Trump任期貿易戰初期就是違背WTO規範，片面無理對中國出口商品加重關稅或其他非關稅貿易手段。

然而真正懂經濟學邏輯者看法多如我當時寫下的預判一樣 — 如果美國以關稅手段要抑制中國出口經濟，但關稅提高幅度不夠大不夠全面的話，則中美之間的貿易逆差狀況不但不會縮減，反而在某些不同彈性系數之下會增加。（見圖）

（中國出口美國統計圖）

反之，美國經濟將因自身對中國的片面關稅障礙而受創。

更進一步，若美國政客傻到真的將制裁關稅提到夠高，足以發生抑制中國出口額的效果，則美國經濟將必須付出重大代價，其中包括美元地位將大幅動搖。如前述貨幣政策問題，不但聯邦政府利息支出將壓垮政府財政，州政府乃至市政府破產潮亦不遠。故，我們看到即便是Trump也被迫停止更瘋狂的關稅壁壘措施。

b 再以半導體產業的光刻機為例，美國施壓荷蘭ASML禁止出貨中國廠商已經付費採購的光刻機，其結果反而是給中國光刻機或EDA廠商創造市場，協助排除了原本ASML強力的競爭。從經濟學角度來看這是一件很諷刺事情。

這是因為全球光刻機市場是一個高度技術集成的天然寡頭壟斷市場，除非有類似當年ASML與日本佳能之間的技術彎道超車（浸潤式UV光刻技術）特殊情況發生，否則後來者都會因為技術認證與攻克的巨大前期投資成本而被排除於競爭之外。

然而，從經濟學競爭的角度看，美國禁止ASML對中國出口，結果反而是讓中國半導體製造廠被迫轉向投資與採購其他中國光刻機供應商，使得原本在市場上幾乎無競爭力的後者，因美國的禁令創造的「競爭真空」環境而有了成長空間。

因此我們放大時間尺度來看，20年、30年後如果中國半導體設備商有了長足的進展，肯定要回過頭感謝美國政府政府的錯誤干預所創造的商機。

說到商機身為投資人的我們可以注意，在上述政客的錯誤決策中，一些轉瞬即逝的投資機會也會因政府干預而起。例如下一點。

c. Super Micro 間諜晶片事件，2018年10月美國知名商業性雜誌Bloomberg刊登新聞「The Big Hack: How China Used a Tiny Chip to Infiltrate U.S. Companies」聲稱Super Micro這家公司利用一顆米粒大小的間諜晶片替中國政府竊取資訊。

姑且不提一顆米粒大小，本身毫無無線射頻天線的晶片在當時技術上幾乎不可能竊取什麼資訊，2年多後海潮退去，不但美國政府或Bloomberg都未提出更進一步有力證據，整件事甚至根本就被遺忘。

當年我不但寫了幾篇文章駁斥這種謬論栽贓。還親自動手買入這家粉紅單公司，短短三天就賺了台轎車。

香港2019年暴動事件、2021年新疆奴隸棉花事件、最近新冠病毒向中國求償事件...等，我們都可以看到美國政客在試圖提高中國競爭成本的過程，會創造大大小小系統性或個體性的災難風險，例如前述Super Micro因栽贓性假消息股價從$20.61美元在一兩日內崩跌至$13左右，但隨著栽贓者無力提供更多證據，市場回歸均衡的過程，截至2021年5月28日，Super Micro股價已經來到$35。

這是說，某些因政治干預造成的個體性或系統性風險，雖然屬於不可預測的風落（windfall），但其中不乏類似Super Micro的例子，在隨後回到正常的價值位置。如W. Buffett所言：市場短期是投票機，但長期是磅秤。

d. 美國知名橋水基金創辦人Ray Dalio在其將於2021年11月初版的書籍」The Changing World Order」 已提前公開的第七章」US-China Relations and Wars」提出綜合國力歷史計算與國力表（見圖）

提出美國正處於信用擴張後期的大國階段，而歷史上處於此階段與新興國力上生階段的國家一旦發生國力曲線交叉時，多半發生大規模戰爭以重新均衡雙方與整體國際關係。

依其推論，中美兩國發生戰爭的風險來到史上最高點。

但這部分我持較保留態度，特別是新任President Biden政府的高達$6 triilion美元的聯邦預算案出台，我們注意到一者，美國聯邦政府支出繼續維持二次世界大戰以來的GDP高佔比--達25%，二者，預算增幅最大均在健康醫療（成長23.1%）、商務（27.7％）與環保（21.3％），然在國防（1.6％）與國家安全（0.2％）幾乎未有成長，甚至計入通貨膨脹因素，後二部門的預算是實質減少的。因此可推估此任政府對發生大型戰爭的預期心理。

四、 變種病毒的不確定性

這是最後最難評估的風險，在現階段的資產配置決策中不可忽略卻又幾乎難以估計。拔高到國家決策層面來看，這也是中國面對的最棘手風險之一。

結論：

以上是我從經濟學角度出發，非常簡略地預測中國在疫情後將面對的國內外經濟環境與挑戰。其中任何一項單獨提出要深入探討都會是長篇大論。還有一些我認為相對重要性較低的現象與局限條件轉變，本文也尚未涵蓋。

BTW，最後多提一句台灣獨有的風險：後疫情時代是否接種過疫苗有可能在相當時間內成為國際旅遊的必要條件。然如果台灣政府真的壓寶在台灣國產疫苗上，則在現今環境下有沒有可能不被世界多數國家組織承認？會是一個額外的成本。

參考文獻：

*  The Wall Street Journal, 「Biden is the $6 Trillion Man」 (May 28, 2021), https://www.wsj.com/articles/biden-is-the-6-trillion-man-11622241749
*  The Financial Times, 「The summer of inflation: will central banks and investors hold their nerve?」 (May 15, 2021), https://www.ft.com/content/414e8e47-e904-42ac-80ea-5d6c38282cac
*  Ronald Coase, 「The Problems of Social Cost」 (1960)
*  Ray Dalio, 「The Changing World Order: Why Nations Succeed and Fail」 (2021)
*  Irving Fisher, 「The Money Illusion」 (1928)
*  Mundell, Robert A. (1963). "Capital mobility and stabilization policy under fixed and flexible exchange rates". Canadian Journal of Economics and Political Science. 29 (4)
*  Milton Friedman and Anna Schwartz, 「A Monetary History of the US, 1867-1960」 (1963)
*  Milton Friedman, 「Money and the Stock Market」 The Journal of Political Economy, Vol. 96, No. 2 (Apr., 1988), pp. 221-245 「
*  Allan Meltzer, 「Learning about Policy from Federal Reserve History」 (Spring 2010)
*  Armen A. Alchian, 「Effects of Inflation Upon Stock Prices" (1965)
*  張五常, 「Will China Go Capitalist?」 (1982)
*  張五常, 「The Economic Structure of China」 (2007)
*  Ronald Coase and Ning Wang, 「How China Became Capitalist」 (2012)
*  Alfred Marshall, 「Principles of Economics (8th ed.)」 (1920)

文章連結：

https://bit.ly/3vD1B2o

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

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the changing world order raydalio chapter 1

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#Raydalio #thechangingworldorder

注意!! 影片中的防塵蓋不小心裝反了，正確安裝方式請觀看下列影片。
A little mistake, the dust cover was installed wrongly, please check this video to install the dust cover in correct way.
▸▸▸https://youtu.be/F0JKk5B47H4

- 目錄 / Menu -
· 射擊測試 / Shot test - 00:20
· 射擊分貝測試(32/30口徑滅音管) / Shot dB test (32/30mm suppressor) - 01:28
· 新版原廠活塞 / New version stock piston - 02:26
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· 新版原廠拉柄頭 / New bolt knobs - 04:39
· 十發初速表現 / Shots velocity performance 10 - 05:13
· 彈匣井鬆緊調整 / Mag well tightness adjustment - 06:06
· 取出活塞汽缸組 / Bolt set removal - 06:35
· 新版橡膠防塵護蓋 / New version dust cover - 06:48
· SRS-A2 22吋標準版 / SRS-A2 standard version - 07:55
· 特別感謝 / Special thanks - 08:19
· SRS-A2 16/22吋寫真 / Close up looks of SRS A2 16"/22" - 08:37

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感謝代理商楓葉精密與Simon哥給予合作機會，借我這幾把拍攝影片，SRS A2下星期台灣正式上市，有興趣的朋友們，歡迎到CTM Airsoft官方網站預購，謝謝您的觀看!
Thanks Maple leaf and Simon to give me a big opportunity to borrow these SRS A2 and make this video. SRS AW will b launched in Taiwan next week. For those who are interested in owning SRS A2, you can also pre-order them from CTM Airsoft. Thanks for watching.

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